Our minds are adapted for the real 3D world we inhabit (both by genetic evolution and training from experience). Higher dimensions are abstractions only. However, I knew someone once who claimed he had trained himself to visualize higher dimesnions. I suppose it's possible. Fortunately, higher dimensional mathematics does not require visualization, just a computers only need 1D memory to do 3D CAD programs.

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QUOTE(Rick @ Dec 12, 2006, 12:02 PM)

Our minds are adapted for the real 3D world we inhabit (both by genetic evolution and training from experience). Higher dimensions are abstractions only. ..

Abstraction. Concrete. A professor was asked to define the difference between them. He said: "My wife is a bad cook. When she thinks about baking a cake; that is an abstraction. When she bakes a cake; that is concrete."

If I can think of a cube moving off into space and beyond my sight, am I thinking in four dimensions?

Our minds are adapted for the real 3D world we inhabit (both by genetic evolution and training from experience). Higher dimensions are abstractions only. ..

Abstraction. Concrete. A professor was asked to define the difference between them. He said: "My wife is a bad cook. When she thinks about baking a cake; that is an abstraction. When she bakes a cake; that is concrete."

If I can think of a cube moving off into space and beyond my sight, am I thinking in four dimensions?

sounds like a 3D object movie in 3 dimensions~ You could visualize a cube moving into space in a 2D environment

To Lindsay and Flex, note that I specifically asked about spatially visualizing in 4D. I'm not asking about spatially visualizing a 3D object in a fourth non-spatial dimension, such as time, which is trivial.

I want to know, if our imagination is infinite, then why can we not imagine in 4 spatial dimensions? Why can't I imagine a hypercube (and not its 3D projection)?

Hey Hey, I'm not sure what you mean since different angles on reality seem to implicitly assume underlying dimensions.

Rick is getting at what I'm after, of evolution and experience limiting our imaginative abilities. Why should our imagination be limited to our perception? Why is our imagination not infinite?

Rick is getting at what I'm after, of evolution and experience limiting our imaginative abilities. Why should our imagination be limited to our perception? Why is our imagination not infinite?

Btw, Rick, I do not believe your friend.

I'm not sure I believe him either, but he was a mathematical genius, so it's possible. Why would he lie?

I can pseudo-visualize 4D by coloring the 4th dimension, but that's also a trivial charting technique. When I try to spatially visualize 4D I feel like I'm spinning over backward and quit. Maybe if I keep trying...

There's a cosmological theory (probably unprovable) that our 3D universe is embedded in higher dimensions inaccessible to us. If there is no way to tell if that is the case, then why speculate about it?

When I try to spatially visualize 4D I feel like I'm spinning over backward and quit. Maybe if I keep trying...

We should explore the methods people use to visualise 4D. Rick, explain, if it's possible, how you try to do this. Can you stop the feeling of spinning over backward by laying down? Or maybe one should try to exacerbate this as part of the visualization process?

If reality (yerrr, I know, what do I mean by reality) involves higher dimensions can we ever hope to visualise reality? Or are we stuck forever with this claymation world? Will the consciousness singularity help with problems like this? How? When?

If reality (yerrr, I know, what do I mean by reality) involves higher dimensions can we ever hope to visualise reality? Or are we stuck forever with this claymation world? Will the consciousness singularity help with problems like this? How? When?

Reality is the union (in the set-theoretical sense) of things that exist. Keep it simple.

One of the things that exists is space, which has three (possibly non-euclidean) dimensions. Because higher dimensions do not exist (there is no credible evidence for them to date), we really don't have a need to "visualize" these abstractions. However, the flexible human mind seems to be able to do that with practice, if some reports are to be believed (e.g. my mathematics teacher who claimed that ability).

So the general inabilty to visualize higher spatial dimensions is not a limitation of consciousness, but of mind (of which the conscious part is structured consciousness).

I believe we do not have the capacity to 'see' or imagine anything beyond the reality we've been brought up in.

case in point: We are not capable of creation. <-- very subjective, but something i firmly believe.If i asked you to draw something no one has ever seen, your first response would be to combine bits and pieces of creatures you've seen. Thats not creation, thats simply regurgitation of information already present in the brain.

That is the way our society has progressed through time, we learn something, we extrapolate from that new realisation and we figure out whats the next step. Someone from the past who sees the level of technology we have achieved will believe its magic because there were too many progressive steps skipped for him to have an understanding of what he's seeing.

But after thats all said and done, drugs and/or meditation may help us 'see' that 4th dimension. I consider that to be our inner-space.

If reality (yerrr, I know, what do I mean by reality) involves higher dimensions can we ever hope to visualise reality? Or are we stuck forever with this claymation world? Will the consciousness singularity help with problems like this? How? When?

Reality is the union (in the set-theoretical sense) of things that exist. Keep it simple.

One of the things that exists is space, which has three (possibly non-euclidean) dimensions. Because higher dimensions do not exist (there is no credible evidence for them to date), we really don't have a need to "visualize" these abstractions. However, the flexible human mind seems to be able to do that with practice, if some reports are to be believed (e.g. my mathematics teacher who claimed that ability).

So the general inabilty to visualize higher spatial dimensions is not a limitation of consciousness, but of mind (of which the conscious part is structured consciousness).

I think you're definitely ignoring something here, Rick. First off, are you sure this world is 3D? Since |R| = |R^n| for all n \in {1,2,3,...} [which inherently means there exists a function that isomorphically maps R to R^n], we could even be in 1 dimension but have mathematical relations that are equivalent to our notions of relations with three dimensions. This is all abstraction, though. If you're a constructivist or something like that, you don't have to believe me.

Secondly, we only see the world in any given instance in a 2-dimensional view. Our retinas take in a stream of light, and this stream can only come in two 2-dimensional packets. But, as time moves on [or, rather, as we "move" through time], these become different packets of information, and our unconscious visual abilities are able to construct this into an abstract 3d view, in real-time, based on evolved mathematical abilities prepackaged in our brains to manage the different information between our two eyes.

Are you so sure we cannot visualize 4d, then? If you believe we evolved from primitive animals, then could you believe that we humans have come to our point by fully recognizing our cognitive capability? Personally, I thought that using cross-sections to show how one can understand 3d in terms of 2d is a very good help to understanding 4d in terms of 3d, but it isn't sufficient. I claim to understand 4d as much as I can visualize 3d mentally.

The polytopes are pretty complex because of so many relations to take into account, but understanding, say, a tesseract or a 5-sphere are not challenging to me. Do you really think mathematicians could work all of the mathematics they can without visualizing these things? It may be easy to differentiate a vector function with respect to a certain variable (dimension), but recognizing other underlying relationships requires greater thinking than mental mechanistic procedures. For example, I can confidently tell you that the following sets are equivalent because I understand them both as a unit 5-ball (the interior of a 5-sphere with radius 1):

Abstractions (or any mental constructions) don't exist (except as a physical representation). While every idea can be represented by a binary string, Occam's Razor suggests that we are not living in a computer simulation, but the real thing itself.

As I think I mentioned above, the mind may be flexible enough for some people to effectively visualize higher spatial dimensions. Apparently it has helped HiddenVariable to produce the equation above. The question is "do higher spatial abstractions have any relevance to the physical (real) world?"

The question is "do higher spatial abstractions have any relevance to the physical (real) world?"

Very provoking question Rick!

I think brain can imagine {x,y,z,t} space, where t is time.

I think that man can imagine Minkowski space. I guess Sufi do so when they spin in dance under trance: the neurons network rotates in space, blood distribution in brain changes, space coordinates of neurons interconnected one with another change, the signal passing through them and the electromagnetic fields distribution undergo specific fluctuations. Virtual sequence of events simulated and recorded in the brain may fluctuate, such fluctuation may mix that sequence of imaginary events. Some segments of the brain may record futuristic future (which other alchemic mechanism will strive to convert into reality later on).

And if to follow Lewis Carroll's approach when Alice from one place jumps into another, then possibly she it traveling along one of the axis of the 4 Dimensional cube.

Abstractions (or any mental constructions) don't exist (except as a physical representation). While every idea can be represented by a binary string, Occam's Razor suggests that we are not living in a computer simulation, but the real thing itself.

As I think I mentioned above, the mind may be flexible enough for some people to effectively visualize higher spatial dimensions. Apparently it has helped HiddenVariable to produce the equation above. The question is "do higher spatial abstractions have any relevance to the physical (real) world?"

If we have a group of string theorists and quantum theorists and the like pondering about possible dimensions, then it probably does have relevance to the physical world. In fact, many equations supposedly governing physical activity include a variable of time, and more complex mathematics use higher dimensional manifolds and other tools to approach the question of how things work.

It may not have practicality in everyday life, but it has attainable potential, like E=Mc^2 leading up to nuclear technology.

Time can disappear from physics. Everywhere the symbol "t" appears, replace it with an equivalent expression, e.g., solve the kinetic energy expresson (E = m * v ^ 2 /2) for t where v = d / t. Nobody would do physics this way because it would be incredibly complex, but it shows that time may not be an actual physical dimension the way x, y, and z (spatial directions) may be.

As for the higher dimesions having application in string theory, that is yet to be demonstrated. String theory makes no testable predictions.

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Rick writes:

QUOTE

...the mind may be flexible enough for some people to effectively visualize higher spatial dimensions....The question is "do higher spatial abstractions have any relevance to the physical (real) world?"

Rick, what is a "spatial abstraction"?

IMHO, as my singnature indicates, I look on the cosmos, space/time, all that we can imagine, the mystery of it all, and beyond as being = to GOD.

Abstraction is mental modeling that simplifies some aspect of the world for more effective thinking. For example, an electrical schematic diagram is based on an abstraction of the physical electrical circuit it represents.

Spatial abstraction is thinking in a simplified way about space and spatial dimensions. Our brains are wired to think in 3D fairly easily, but some mathematicians seem to be able to train their brains to think in higher dimensional spatial abstractions.

You could take that as evidence against string theory (or at least other dimensions).

The article may mean that "things" can only exist within a very small interval in the direction of another dimension, if there is "another." For example, there is controversy over when the big bang/creation occurred. So the interval of time that "things" could exist on, theoretically, would be at least anywhere between that point in time and "now."

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Rick writes

QUOTE

...but some mathematicians seem to be able to train their brains to think in higher dimensional spatial abstractions.

I suspect that pneumatherapy--non-manipulative hypnosis--could be used to help trains "brains". I once used it on a young musician who was having difficulty mastering his memory for pitch. At the time, he was the organist at my church.

One day, after listening to a sermon I gave on THE POWER OF PNEUMATOLGY and its relation to faith healing, in which I mentioned pneumatherapy/hypnotism, he said to me:

"You know, my ambition is that one day I will could be an orchestra conductor. Do you think what you call 'pneumatherapy' could help me develop my memory so I can have what is called 'perfect pitch'? But the idea of anyone controlling my mind frightens me."

Being a bright person, it was easy for me to disabuse him of such non-sense--Interesting, isn't it? how false concepts do hold us back! Soon, he sat in my study, and I began the process I call pneumatherapy.

At the same time that I inducted him to enter the trance state, I made a tape recording for him, which he could play, anytime. As part of the process, I used tuning instruments--tuning forks of the key notes, which he provided for me to use.

"There" I said to him. "Peter, do you hear this?" "Yes." he said.

I said, "This is what A sound's like". I repeated the process with the other notes he provided. "The sound of this note" I said, "is etched in the memory part of your brain. You will remember each I sound. You will recall each of them when you choose to do so, agreed?"

"Yes, I agree" he responded.

For years, now, Peter has been a successful conductor--located in Vancouver--with a great reputation, around the globe. A few years ago, my wife and I, lovers of the music of Vienna, heard him conduct a program based on the music of Johann Strauss, the Waltz King--one of our favourites composers. That was in Toronto's Thompson Hall, twenty minutes from where we live.

Following the concert, we met him back stage. "Thank you" he said. "I still remember the day pneumatherpy helped me achieve perfect pitch."

He told us, "From here, I am off to North Carolina and...."

What a wonderful reward it was to witness the success of a such a great artist.

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Rick, you ask, "So he had tried memorizing those tones on his own, and failed?"

Let's back up, here. Not once, did Peter tell me that he had tried to memorize the tones on his own, and failed. I don't think that this had ever occured to him.

Therefore, I will say this: Whatever he had tried to do, he had failed to do. I would add this: It never occurred to him that he could do something about it until he heard that "sermon". All I did during the pneumatherapy, was remind him of what he was already able to do.

This is the essence of what pneumatherapy is all about: It is simply about reminding people who they already are, anyway. Capice?